Prime Factorization for GCF and LCM

Prime Factorization Method for Finding GCF and LCM

• Prime factorization is a technique used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. It's particularly useful for larger numbers.
• The prime factorization method decomposes each number into its prime factors, which are prime numbers that, when multiplied together, equal the original number.

Finding the GCF using Prime Factorization

• Step 1: Determine the prime factorization of both numbers.
• Step 2: Identify the common prime factors in both factorizations.
• Step 3: Multiply the common prime factors to find the GCF.

Finding the LCM using Prime Factorization

• Step 1: Determine the prime factorization of both numbers.
• Step 2: List the prime factors of both numbers vertically, aligning common factors in columns.
• Step 3: Write down one instance of each prime factor from each column, even if there are duplicates.
• Step 4: Multiply the prime factors written down in Step 3 to obtain the LCM.